Having narrowly beaten Serie A side Atalanta on Friday evening, the Magpies impressively saw off La Liga outfit Athletic Bilbao with a completely different starting XI.
Sven Botman was handed his home debut while Joelinton, Jamaal Lascelles and Bruno Guimarães were among the players called upon by Eddie Howe for the fixture against Marcelino García Toral's side, who finished eighth in Spain's top division last term.
And United made a flying start as Saint-Maximin ghosted past a couple of challenges in the fourth minute before finding Ritchie, who neatly played in Wilson. The England international still had plenty to do, but outmanouvered a defender and slotted home.
Four minutes later, Joelinton chested the ball down for Guimarães, whose 20-yard strike was held at the second attempt by Ander Iruarrizaga.
After something of a lull in proceedings, the visitors began to find their feet and fashioned two opportunities from long range - first through Alejandro Berenguer, whose effort was deflected wide, then Óscar de Marcos, who saw his shot held by Martin Dúbravka.
Then on the stroke of half time, Iñaki Williams broke clear but Emil Krafth - who signed a new one-year contract extension earlier this month - showed superb pace to force him wide, and he fired into the side-netting.
United doubled their lead eight minutes into the second period. Joelinton sent Saint-Maximin away on the left and the Frenchman beat the offside trap before steering a low shot beyond Iruarrizaga.
Good defending by Lascelles and Krafth, who combined to clear off the line from Mikel Vesga's dinked cross, preserved that two-goal advantage, but Raúl García's powerful header in the 64th minute gave Athletic Club a potential route back into the game.
Berenguer almost levelled with a curling strike which clipped a post on its way behind, with Dúbravka at full stretch, then Iñaki Williams was narrowly off target after connecting with Oier Zarraga's ball.
With the visitors now boasting the fresher set of legs, with Howe opting to give his starting XI as many minutes as possible seven days before their league campaign begins, Oihan Sancet bent a shot just wide before, in the 78th minute, Dúbravka parried a stinging effort from the same player then clawed away the loose ball as it threatened to spin into the net.
And the Slovakia international shot-stopper made an even better save two minutes later, blocking with his legs from point blank range to thwart García.
That meant that the Magpies go into next weekend's first Premier League game against newly-promoted Nottingham Forest on the back of two victories against high-level European opposition, and with virtually the whole squad having played a full game ahead of the big kick-off - while there were also late senior debuts for youngsters Lucas De Bolle and Santiago Munõz.
Newcastle United: Martin Dúbravka, Emil Krafth, Jamaal Lascelles (c), Sven Botman, Paul Dummett (Matt Bondswell 70), Joelinton, Bruno Guimarães (Lucas De Bolle 89), Joe Willock, Matt Ritchie, Allan Saint-Maximin (Matty Longstaff 89), Callum Wilson (Santiago Munõz 90)
Subs not used: Mark Gillespie, Alex Murphy, Lewis Miley, Jay Turner-Cooke, Dylan Stephenson